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Seeing as mushroom corals are in fact disc anemones it's entirely possible that what you're seeing are eggs though I would think that the eggs would be a lot smaller and even more likely unable to be seen by the naked eye, but I've done zero research on mushroom reproduction outside of fragmentation. The stuff coming out of the mouths are the mushrooms expelling their guts, not uncommon when they're unhappy it's just a stress response. If there's pedal laceration the purple stuff is probably innards poking out of the wound. It might not hurt to give the shrooms a quick bath in in coral RX to prevent any kind of infection from setting in. What was left on the rock I'm guessing is pieces and parts from the parents. Shrooms are pretty resilient so where there is tissue you should see some babies popping up.

Hopefully they all turn out ok for you, like I said most shrooms are super resilient. There are even stories of people seeding their tanks by throwing one or two in a blender, dumping the mush in the tank, and watching the mushrooms grow rampant. Personally I'd never try that but if there is any truth to that urban legend it speaks to the toughness of a mushroom.

Mushrooms, like all other cnidarians, have exactly one opening in their body. All food goes in the one end, and all eggs and poo come out that same opening. Many can and do bud from the foot, but those aren't eggs that they bud off.